Projectile problem -- How much to increase Vi to reach a farther target?

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A missile launched at a 45-degree angle needs to increase its initial velocity to hit a target at 675 km, compared to 300 km. The correct calculation shows a 50% increase in velocity, while one participant initially calculated a 44.5% increase. The discrepancy was attributed to potential numerical errors in the calculations. The formula used for range assumes constant gravitational acceleration, which may not apply at higher altitudes. Ultimately, the participant was able to resolve the issue and find the correct answer.
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Homework Statement


A missile is launched from the ground making 45 degree with the horizontal to hit a target at a horizontal distance of 300 km. If it is required to hit a target at a horizontal distance of 675 km launched at same angle with horizontal, find the percentage change in its velocity of projection. (Answer is 50% increase)

Homework Equations

The Attempt at a Solution


I did it like this but I got 44.5% whereas the answer is 50%

So I did it like this...
R= u²sin2∅/g
I put R= 300km and 675km in the given formula in two equations...
I got √100/3 and √75
Therefore to find % increase
√100/3 divided by √75 * 100
I got 44.5%
But the answer is 50%...please help
 
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D.Man Hazarika said:

Homework Statement


A missile is launched from the ground making 45 degree with the horizontal to hit a target at a horizontal distance of 300 km. If it is required to hit a target at a horizontal distance of 675 km launched at same angle with horizontal, find the percentage change in its velocity of projection. (Answer is 50% increase)

Homework Equations

The Attempt at a Solution


I did it like this but I got 44.5% whereas the answer is 50%

So I did it like this...
R= u²sin2∅/g
I put R= 300km and 675km in the given formula in two equations...
I got √100/3 and √75
Therefore to find % increase
√100/3 divided by √75 * 100
I got 44.5%
But the answer is 50%...please help

Such ranges and launch angles usually suggest that the rocket gains a relatively large altitude before hitting its target. Your range formula assumes that g is constant, which is OK for problems where the projectile remains close to the surface of the earth. For projectiles which travel high in the atmosphere, I'm sure this formula must be modified.

The variation of g with altitude is discussed in this article:

http://en.wikipedia.org/wiki/Gravity_of_Earth

This might be the source of the discrepancy of your calculation with the answer key.
 
Look I am confused I just need u to show me the steps of doing this sum...
 
SteamKing said:
This might be the source of the discrepancy of your calculation with the answer key.
No, it's just numerical error.
D.Man Hazarika said:
I got √100/3 and √75
I don't understand how you got those. Please post all steps.
 
OK thanks anyways I got the answer
 

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